let Y be non empty set ; :: thesis: for a being Function of Y,BOOLEAN
for G being Subset of (PARTITIONS Y)
for A, B being a_partition of Y holds 'not' (All ((All (a,A,G)),B,G)) = Ex ((Ex (('not' a),A,G)),B,G)
let a be Function of Y,BOOLEAN; :: thesis: for G being Subset of (PARTITIONS Y)
for A, B being a_partition of Y holds 'not' (All ((All (a,A,G)),B,G)) = Ex ((Ex (('not' a),A,G)),B,G)
let G be Subset of (PARTITIONS Y); :: thesis: for A, B being a_partition of Y holds 'not' (All ((All (a,A,G)),B,G)) = Ex ((Ex (('not' a),A,G)),B,G)
let A, B be a_partition of Y; :: thesis: 'not' (All ((All (a,A,G)),B,G)) = Ex ((Ex (('not' a),A,G)),B,G)
Ex (('not' (All (a,A,G))),B,G) = Ex ((Ex (('not' a),A,G)),B,G) by BVFUNC_2:18;
hence 'not' (All ((All (a,A,G)),B,G)) = Ex ((Ex (('not' a),A,G)),B,G) by BVFUNC_2:18; :: thesis: verum